1. Field of the Present Invention
The present invention relates to a Direction-Of-Arrival estimating device that estimates arriving waves by use of a sensor array.
2. Description of the Related Art
The Direction-Of-Arrival (which will hereinafter be abbreviated to DOA) estimation using the sensor array is based on three typical well-known algorithms such as a digital-beam-former (which will hereinafter be abbreviated to DBF) method, an eigen-space-method (which will hereinafter be abbreviated to ESM) and a maximum-likelihood (which will hereinafter be abbreviated to ML) method.
The DBF method is typified by a CAPON method, a Linear Prediction method, etc. The ESM is typified by a MUSIC (Multiple Signal Classification) method, an ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method and a Propagator method. Further, the ML method is typified by a MODE (Method of Direction Estimation) etc.
The algorithms given above have, however, a property that DOA estimation accuracy gets higher in the sequence such as DBF<ESM<ML, and on the other hand, along with this, a calculation quantity required for the DOA estimation becomes larger in the same sequence. With this property, in the case of considering the algorithm as, for example, an on-vehicle application, a clock of an on-vehicle CPU (Central Processing Unit) is on the order of 80 MHz at the maximum, and hence even implementation of the ESM requiring decomposition of an eigenvalue is difficult.
Proposed as a method of solving this difficulty is the Propagator method categorized as the ESM that does not require the decomposition of the eigenvalue or an Orthonormal Propagator Method (which will hereinafter be abbreviated to OPM) defined as an improved version of this Propagator method. It is, however, hard to say that those algorithms actualize the sufficient DOA estimation accuracy.
Herein, an explanation of how the DOA estimation is performed by the conventional DOA estimation device will be made with reference to FIG. 7 by exemplifying a case of a radar system constructed of linear array antennas. FIG. 7 illustrates a case in which NS-pieces (≦NA−1) of independent signals get incident at angles θm different from each other (which are based on a vertical direction of an antenna-axis (the Y-axis shown in FIG. 7) upon the linear array antennas having an antennal element count NA and an equal element interval d. “Xm(t)” represents a baseband component of the arriving signal from, e.g., an m-th target (m=1, . . . , NS), and “vn(t)” represents an output signal obtained by demodulating an input signal in an n-th antenna element (n=1, . . . , NA).
At this time, the output signal vn(t) is expressed as by the following formula (1.1).
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          1                ]                                                                                  v            n                    ⁡                      (            t            )                          =                                            ∑                              m                =                1                                            N                S                                      ⁢                                                  ⁢                                                            x                  m                                ⁡                                  (                  t                  )                                            ⁢                              exp                ⁡                                  (                                      jϕ                                          n                      ⁢                                                                                          ,                      m                                                        )                                                              +                                    n              n                        ⁡                          (              t              )                                                          (        1.1        )                                          ϕ                      n            ,            m                          ≡                                            2              ⁢              π                        λ                    ⁢                      (                          n              -              1                        )                    ⁢          d          ⁢                                          ⁢          sin          ⁢                                          ⁢                      θ            m                                              (        1.2        )            
In the formulae (1.1) and (1.2), “nn(t)” represents a noise signal, “Φn,m” represents a reception phase of an m-th wave in the element n when based on the element 1, and “λ” represents a wavelength of a carrier wave.
If these formulae are further expressed as vectors, the following formulae (1.3)-(1.6) are acquired.
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          2                ]                                                                      v          ⁡                      (            t            )                          =                              [                                                                                                                              ∑                                                  m                          =                          1                                                                          N                          S                                                                    ⁢                                                                                          ⁢                                                                                                    x                            m                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  exp                          ⁡                                                      (                                                          j                              ⁢                                                                                                                          ⁢                                                              ϕ                                                                  1                                  ,                                  m                                                                                                                      )                                                                                                                +                                                                  n                        1                                            ⁡                                              (                        t                        )                                                                                                                                          ⋮                                                                                                                                                ∑                                                  m                          =                          1                                                                          N                          S                                                                    ⁢                                                                                          ⁢                                                                                                    x                            m                                                    ⁡                                                      (                            t                            )                                                                          ⁢                                                  exp                          ⁡                                                      (                                                          jϕ                                                                                                N                                  A                                                                ,                                m                                                                                      )                                                                                                                +                                                                  n                                                  N                          A                                                                    ⁡                                              (                        t                        )                                                                                                                  ]                    =                                    Ax              ⁡                              (                t                )                                      +                          n              ⁡                              (                t                )                                                                        (        1.3        )                                          A          ≡                      [                                          a                ⁡                                  (                                      θ                    1                                    )                                            ,                                                          ⁢              …              ⁢                                                          ,                                                          ⁢                              a                ⁡                                  (                                      θ                                          N                      S                                                        )                                                      ]                          =                  [                                                                      exp                  ⁡                                      (                                          jϕ                                              1                        ,                        1                                                              )                                                                              ⋯                                                              exp                  (                                      jϕ                                          1                      ,                                              N                        S                                                                              )                                                                                    ⋮                                                                                                                          ⋮                                                                                      exp                  (                                      jϕ                                                                  N                        A                                            ,                      1                                                        )                                                            ⋯                                                              exp                  (                                      jϕ                                                                  N                        A                                            ,                                              N                        S                                                                              )                                                              ]                                    (        1.4        )                                          x          ⁡                      (            t            )                          ≡                              [                                                            x                  1                                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢              ⋯              ⁢                                                          ⁢                                                x                                      N                    S                                                  ⁡                                  (                  t                  )                                                      ]                    T                                    (        1.5        )                                          n          ⁡                      (            t            )                          ≡                              [                                                            n                  1                                ⁡                                  (                  t                  )                                            ⁢                                                          ⁢              ⋯              ⁢                                                          ⁢                                                n                                      N                    S                                                  ⁡                                  (                  t                  )                                                      ]                    T                                    (        1.6        )            
In the formulae (1.3)-(1.6), “v(t)” represents an output signal vector, “x(t)” represents a baseband vector, “n(t)” represents a noise vector, “a(θm)” represents a mode vector (direction vector), and “T” represents transposition.
Then, supposing that there is no correlation between x(t) and n(t), when calculating covariance matrixes of v(t) from the formula (1.3), the matrixes are expressed by the following formulae (1.7) and (1.8).
[Mathematical Expression 3]Rvv=E{v(t)vH(t)}=ARxxAH+σ2I  (1.7)Rxx=E[x(t)xH(t)]  (1.8)
In the formulae given above, “Rvv” is the covariance matrix of (NA×NA) dimensions, and “Rxx” is the covariance matrix of the baseband signal of (NS×NS) dimensions. Further, “E{·}” represents an expected value (ensemble or time average), “H” represents complex conjugate transposition, “σ2I” represents a covariance matrix of the noise vector, “I” represents a unit matrix, and “σ2” represents dispersion (noise electric power) of the noise vector n(t). Then, this covariance matrix Rvv is the matrix of the basic DOA estimation target formula.
Thus, in the linear array antennas shown in FIG. 7, in the case of performing the DOA estimation by the DBF or the ESM, to begin with, it is required that the signal covariance matrix Rvv of (NA×NA) be calculated.
The signals received by the radar system are, however, nothing but the signals transmitted from the same signal source and reflected by the target, so that a rank of the covariance matrix Rvv of NA×NA is Ns. Accordingly, even when performing an operation such as an inverse matrix operation and eigenvalue decomposition directly about Rvv, the covariance matrix Rvv becomes a singular matrix and can not therefore be obtained proficiently. This leads to a difficulty that the DBF and the ESM are applied directly to the DOA estimation in the radar system. Further, the ML is the optimizing calculation in which singular value decomposition having a calculation load substantially proportional to NA3 is included in a loop, and hence the implementation is in fact difficult.
Such being the case, for obviating the problem, the prior art has a scheme to restore a hierarchy of the covariance matrix Rvv by utilizing a spatial average method (which will hereinafter be referred to as Forward-Backward Spatial Smoothing (FBSS)) with respect to Rvv. The FBSS is the spatial average method that is a combined version of a Forward Spatial Smoothing (FSS) method of taking submatrixes (NA−NP+1 pieces of submatrixes can be acquired) of NP×NP in a main diagonal direction of Rvv, and adding and averaging the submatrixes, and a Backward Spatial Smoothing (BSS) method of performing the same operation by inverting an array reference point.
Then, the prior art implements the DOA estimation with respect to RvvFBSS of NP×NP that is calculated by the spatial average method (FBSS) in a way that utilizes the CAPON method typified by the DBF and the MUSIC method typified by the ESM. The following formula (1.9) is a calculation formula of calculating an angle spectrum (angle distribution) based on the CAPON method.
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          4                ]                                                                                  P            CAPON                    ⁡                      (            θ            )                          =                  1                                                                                          a                    H                                    ⁡                                      (                    θ                    )                                                  ⁡                                  [                                      R                    vv                    FBSS                                    ]                                                            -                1                                      ⁢                          a              ⁡                              (                θ                )                                                                        (        1.9        )            
The CAPON method involves, as shown in the formulae given above, calculating an angle spectrum PCAPON(θ) from the covariance matrix RvvFBSS and the mode vector a(θ), whereby the direction of arrival is estimated from a peak position when changing “θ”.
The following formulae (1.10) and (1.11) are calculation formulae of calculating the angle spectrum (angle distribution) by use of the MUSIC method.
                    [                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          5                ]                                                                      R          vv          FBSS                =                                            E              S                        ⁢                          Λ              S                        ⁢                          E              S              H                                +                                    σ              2                        ⁢                          E              N                        ⁢                          E              N              H                                                          (        1.10        )                                                      P            MUSIC                    ⁡                      (            θ            )                          =                                                            a                H                            ⁡                              (                θ                )                                      ⁢                          a              ⁡                              (                θ                )                                                                                        a                H                            ⁡                              (                θ                )                                      ⁢                          E              N                        ⁢                          E              N              H                        ⁢                          a              ⁡                              (                θ                )                                                                        (        1.11        )            
In the MUSIC method, the angle spectrum PMUSIC(θ) shown in the formula (1.11) is obtained by using a matrix EN acquired by conducting the eigenvalue decomposition of RvvFBSS as shown in the formula (1.10). “EN” represents the matrix formed by eigenvectors in a noise eigenspace, “ES” represents a matrix formed by eigenvectors in a signal eigenspace, then, if θ is coincident with an angle-of-arrival θm of the arriving wave, a sharp peak appears in the angle spectrum PMUSIC(θ), and the direction of arrival is estimated from a position of this peak.
Thus, the conventional DOA estimation method needs the operation of, at first, performing the multiplications (NA×NA) times for forming Rvv, the operation of inverting the array reference point by the FBSS ((NA×NA) matrix is multiplied twice), the operation of adding the submatrixes 2(NA−NP−1) times, and the operation of conducting the eigenvalue decomposition of RvvFBSS.
Namely, the conventional DOA estimation methods using the sensor array include none of methods capable of performing the estimation at a high speed with high accuracy and with a small calculation quantity. In this type of conventional DOA estimation technology, an estimation method utilizing the BS-MUSIC method by use of the array antennas as a sensor array is proposed (refer to Patent document “Japanese Patent Application Laid-Open Publication No. 2000-196328”).